Constructive Solutions to the Riemann–Hilbert Problem and Middle Convolution
نویسندگان
چکیده
منابع مشابه
On the middle convolution
In [9], a purely algebraic analogon of Katz’ middle convolution functor (see [12]) is given. It is denoted by MCλ. In this paper, we present a cohomological interpretation of MCλ and find an explicit RiemannHilbert correspondence for this functor. This leads to an algorithm for the construction of Fuchsian systems corresponding to irreducible rigid local systems under the Riemann-Hilbert corres...
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The parameter q is called an accessory parameter. Although the local monodromy (local exponent) is independent of q, the global monodromy (e.g. the monodromy on the cycle enclosing two singularities) depends on q. Some properties of Heun’s equation are written in the books [21, 23], but an important feature related with the theory of finite-gap potential for the case γ, δ, ǫ, α−β ∈ Z+ 12 (see [...
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We use the middle convolution to obtain some old and new algebraic solutions of the Painlevé VI equations.
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This is an expository account of Katz’s middle convolution operation on local systems over P − {q1, . . . , qn}. We describe the Betti and de Rham versions, and point out that they give isomorphisms between different moduli spaces of local systems, following Völklein, Dettweiler-Reiter, Haraoka-Yokoyama. Kostov’s program for applying the Katz algorithm is to say that in the range where middle c...
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In this paper we develop constructive invertibility conditions for the twisted convolution. Our approach is based on splitting the twisted convolution with rational parameters into a finite number of weighted convolutions, which can be interpreted as another twisted convolution on a finite cyclic group. In analogy with the twisted convolution of finite discrete signals, we derive an anti-homomo...
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ژورنال
عنوان ژورنال: Journal of Dynamical and Control Systems
سال: 2015
ISSN: 1079-2724,1573-8698
DOI: 10.1007/s10883-015-9306-3